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Algebraic Attacks on Summation Generators
[chapter]

2004
*
Lecture Notes in Computer Science
*

We apply the

doi:10.1007/978-3-540-25937-4_3
fatcat:fgviepljfbd4hbzpxxnpwu5raq
*algebraic**attacks**on*stream ciphers with memories to the*summation**generator*. ... We also show that the techniques of [6, 2] can be applied to*summation**generators*using 2 k LFSRs to reduce the effective degree of the*algebraic*equation. ... Structure of*summation**generators*In this work, we study the*summation**generator*with the*algebraic**attack*in mind. ...##
###
Algebraic Countermeasure to Enhance the Improved Summation Generator with 2-Bit Memory

2013
*
Journal of Networks
*

This stream cipher was proposed in 2008 to enhance the security of the improved

doi:10.4304/jnw.8.5.977-984
fatcat:kacqzlbwbrds5crrvjr5kemkuu
*summation**generator*against the*algebraic**attack*. ... Recently proposed*algebraic**attack*has been shown to be very effective*on*several stream ciphers. ...*Algebraic**attack**on*stream cipher includes*attacks**on*nonlinear filter*generator*[2] ,*attacks**on**summation**generator*[4] ,*attacks**on*combiners with memory [2] ,*attacks**on*mutually clocked shift register ...##
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Methodes de Resolution et de Discussion des Problemes de Geometrie

1904
*
Mathematical Gazette
*

This is the German edition of a useful introduction to methods of

doi:10.2307/3605178
fatcat:xmfgncy5rfhivbktzmontovr4u
*attacking*the solution of geometrical riders. ... The second treats of*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ... The second treats of*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ...##
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The ANF of the Composition of Addition and Multiplication mod 2 n with a Boolean Function
[chapter]

2005
*
Lecture Notes in Computer Science
*

As an application, the formula for addition modulo 2 n is applied in an

doi:10.1007/11502760_8
fatcat:5ztssiiyerfa7csxa2ddvt47m4
*algebraic**attack**on*the*summation**generator*and the E0 encryption scheme in the Bluetooth keystream*generator*. ... Compact formulas are derived to represent the*Algebraic*Normal Form (ANF) of f (x + a mod 2 n ) and f (x × a mod 2 n ) from the ANF of f , where f is a Boolean function*on*F n 2 and a is a constant of ...*Algebraic**Attack**on*the*Summation**Generator*Consider a*summation**generator*, proposed by Rueppel [25] , that consists of n binary Linear Feedback Shift Registers (LFSR). ...##
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Generic Analysis of Small Cryptographic Leaks

2010
*
2010 Workshop on Fault Diagnosis and Tolerance in Cryptography
*

(Dinur&Shamir): Is a very

doi:10.1109/fdtc.2010.11
dblp:conf/fdtc/DinurS10
fatcat:nnu4sggluzbobgjh4oz623pxe4
*general*key derivation*algebraic**attack**Generalizes*and improves some previous*summation*-based*attacks*such as Integral*Attacks*and Vielhaber's AIDA Was recently used to break ... The*attacker*can obtain*one*bit of output for any chosen plaintext. ... 18 Maxterms for 3-round Serpent: Conclusions: Cube*attacks*seem to be ideal*generic*tools in leakage*attacks*They have the unique property that they can be applied even to poorly understood types of ...##
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Practical attack on NLM-MAC scheme

2014
*
Information Processing Letters
*

The NLM stream cipher designed by HoonJae Lee, SangMin Sung, HyeongRag Kim is a strengthened version of the LM

doi:10.1016/j.ipl.2014.04.010
fatcat:xz7s4baptjef3fbehjpsranvuq
*summation**generator*that combines linear and non-linear feedback shift registers. ... The*attack*needs about n 2 key-stream bits. We also show adversary is able forge any MAC tag very efficiently by having only*one*pair (MAC tag, cipher-text). ... Unfortunately, it is insecure against the correlation and*algebraic**attacks*. In 2000, Hoon Jae Leea and Sang Jae Moon proposed an improved*summation**generator*with 2-bit memory (5) . ...##
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A novel architecture with scalable security having expandable computational complexity for stream ciphers

2017
*
Facta universitatis - series Electronics and Energetics
*

Contemporary stream cipher designs are highly vulnerable to

doi:10.2298/fuee1704459s
fatcat:okt27kydlrcspf6iqawusiy2z4
*algebraic*cryptanalysis based*on*linear*algebra*, in which the inputs and outputs are formulated as multivariate polynomial equations. ... Recently, Addition Modulo has been suggested over logic XOR as a mixing operator to guard against such*attacks*. ... Later, the*attack*was*generalized*and applied*on*stream ciphers and block ciphers [5] [6] [7] . ...##
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Page 69 of Mathematical Gazette Vol. 3, Issue 46
[page]

1904
*
Mathematical Gazette
*

The second treats of

*summation*, the J. Bernouilli Function, and Euler’s*summation*formula with its applications. ... Graphs are well to the fore in dealing with equations*generally*, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter*on*involution ...##
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Association of Teachers of Mathematics in the Middle States and Maryland. Bulletin No. I

1904
*
Mathematical Gazette
*

The second treats of

doi:10.2307/3605177
fatcat:rkechftcd5bn7fuodu72rl6pba
*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ... The second treats of*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ... , continued fractions,*summation*of series, theory of numbers, determinants, and theory of equations. ...##
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Aufgaben aus der Niederen Geometrie. By I. Alexandroff. Pp. v, 123. 1904. (Teubner.)

1904
*
Mathematical Gazette
*

The second treats of

doi:10.1017/s0025557200114755
fatcat:xe2pjhdhsjfczaeity5fcj7owu
*summation*, the J. Bernouilli Function, and Euler’s*summation*formula with its applications. ... Graphs are well to the fore in dealing with equations*generally*, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter*on*involution ...##
###
Lehrbuch der Differenzenrechnung. By D. Seliwanoff. Pp. vi, 92. 1904. (Teubner.)

1904
*
Mathematical Gazette
*

The second treats of

doi:10.1017/s0025557200114767
fatcat:ngt2usneqndxvhbtxiurixlio4
*summation*, the J. Bernouilli Function, and Euler’s*summation*formula with its applications. ... Graphs are well to the fore in dealing with equations*generally*, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter*on*involution ...##
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Lehrbuch der Analytischen Geometrie. By O. Fort and O. Schlomilch. Vol. I. Analytische Geometrie der Ebene. 7th edition. Revised by R. Heger. 1904. (Teubner.)

1904
*
Mathematical Gazette
*

*summation*, the J. Bernouilli Function, and Euler’s

*summation*formula with its applications. ... Graphs are well to the fore in dealing with equations

*generally*, the theory of the irrational number, derivatives, multiple roots, Sturm’s theorem, and discontinuous functions, The chapter

*on*involution ...

##
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A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
[article]

2019
*
arXiv
*
pre-print

In cryptography, this interpretation can be used to design

arXiv:1909.08901v1
fatcat:j3u4gljhxjehhikcmvflwq3yqu
*attacks**on*EC-DLP. ... Presently, the best known*attack*algorithm having a sub-exponential time complexity is through the implementation of*Summation*Polynomials and Weil Descent. ... We would like to thank the High Performance Computing (HPC) facility of University of L'Aquila, which enabled us to implement our algorithm*on*MAGMA and run the experiments to validate our results. ...##
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A Simple Algebraic Representation of Rijndael
[chapter]

2001
*
Lecture Notes in Computer Science
*

We show that there is a very straightforward closed

doi:10.1007/3-540-45537-x_8
fatcat:6moz65bmozgmxhj7b2wo7pkfi4
*algebraic*formula for the Rijndael block cipher. ... This formula is highly structured and far simpler then*algebraic*formulations of any other block cipher we know. ... There are some*general*techniques that work for any block cipher, but these do not lead to practical*attacks*. ...##
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Advanced Course in Algebra

1904
*
Mathematical Gazette
*

The second treats of

doi:10.2307/3605179
fatcat:lk2htzc4mjhf7hzpvjrcmrsf7a
*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ... This is the German edition of a useful introduction to methods of*attacking*the solution of geometrical riders. ... The second treats of*summation*, the J. Bernouilli Function, and Euler's*summation*formula with its applications. ...
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